Sauron is obviously pretty clear (but I think even Sauron is a fallen angel of sorts?), but the rest of the story is about how everyone can be corrupted by power and defeated by despair. Even Gandalf, another 'angel' of sorts, could be corrupted. Sauruman, another being like Gandalf and the latter's superior, was corrupted.

In the end, the difference between the heroes and villians is whether they are wise enough to avoid exposing themselves to the corruption of power, and some cross that line. Finally, the ring is destroyed by someone who was thoroughly corrupted but, kept away from power and treated with love and mercy, was able to heal somewhat for a time.